Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.9 years, and standard deviation of 2.9 years. If you randomly purchase 9 items, what is the probability that their mean life will be longer than 14 years

Answer 1

0.4588

Explanation:

When we have random sample, the z score formula we use is:

z = (x-μ)/σ/√n

where x is the raw score = 14

μ is the population mean = 13.9

σ is the population standard deviation = 2.9

n is random number of samples = 9

z = 14 - 13.9/2.9/√9

z = 0.1/2.9/3

z = 0.10345

Probability value from Z-Table:

P(x<14) = 0.5412

P(x>14) = 1 - P(x<14) = 0.4588

The probability that their mean life will be longer than 14 years is 0.4588